A Robust and Accurate Convective-Pressure-Split Approximate Riemann Solver for Computation of Compressible High Speed Flows

摘要

The Harten-Lax-van Leer (HLL) based Convective-Pressure-Split (CPS) approximate Riemann solver (HLL-CPS) is a popular upwind scheme designed to discretize the Euler system of equations that governs compressible high speed flows. However, the HLL-CPS scheme is known to possess two major drawbacks: high numerical dissipation on shear waves and susceptibility to numerical shock instability. In this paper, we demonstrate that the accuracy of the shear waves can be recovered by directly employing an HLLC-type anti-diffusive term in the discretized pressure system of the HLL-CPS scheme. We show that the resulting scheme, termed HLLC-CPS, can be made shock stable by selectively controlling this anti-diffusive term in the vicinity of a numerical shock front using a pressure-ratio based control parameter. Numerical results show the efficacy of the proposed scheme.